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## Working With Simplified Quadratic Equations

#### High School - HSN-CN.C.7

How to Simplify Quadratic Equations - We all have studied quadratic equations quite a few times. A quadratic equation is used in many complex problems to simplify them. A quadratic equation can be written as ax2 + bx + c, where a = 0 To solve a quadratic equation, there are three methods to follow; factoring method, the quadratic formula method, and completing the square method. Factoring - Leaving zero on one side, take all the terms on one side. Now Factor. Set each factor to zero and solve each of these equations. Now make sure that the equation is satisfied by putting the answer in the original equation. The quadratic formula - Another method of solving quadratic equations involves the use of the following formula: x = (-b ± √ - 4ac / 2a) Completing the square - Convert the equation in the form; ax2 + bx = – c. Ensure that a = 1 (if not, multiply the equation by 1/a before proceeding). With the value of b derived from the new equation, add (b/2)2 to both sides of the equation and make it a perfect square. Now you can make square roots of both sides of the equation. Solve the resulting equation.

### Printable Worksheets And Lessons  #### Homework Sheets

Working with quadratics in straight format.

• Homework 1 - Most of these are solving by factoring.
• Homework 2 - Remeber to factor in the same fashion.
• Homework 3 - Start all of these by moving all terms to one side of the equals symbol.

#### Practice Worksheets

These are all followed with detailed explanations. This should help it click faster.

• Practice 1 - Solve all the quadratic equations.
• Practice 2 - In most cases you will use addition or subtraction of terms in the first step.
• Practice 3 - After everything is to one side, factor it to the end.

#### Math Skill Quizzes

I would definitely have some scrap paper available for these quizzes.

• Quiz 1 - Your thrid step should be to make the factor value equal to zero.
• Quiz 2 - Then list the solutions to the original.
• Quiz 3 - Solve this bad boy: X2 + 24x + 140 = -4